One of your employees has suggested that your company develop a new product. You

Question

One of your employees has suggested that your company develop a new product. You decide to take a random sample of your customers and ask whether or not there is interest in the new product. The response is on a 1 to 5 scale with 1 indicating "definitely would not purchase"; 2, "probably would not purchase"; 3, "not sure"; 4, "probably would purchase"; and 5, "definitely would purchase." For an initial analysis, you will record the responses 1, 2, and 3 as "No" and 4 and 5 as "Yes."

Suppose that after reviewing the results of a previous survey, you proceeded with preliminary development of the product. Now you are at the stage where you need to decide whether or not to make a major investment to produce and market it. You will use another random sample of your customers, but now you want the margin of error to be smaller. What sample size would you use if you wanted the 95% margin of error to be 0.025 or less? (Round your answer up to the nearest whole number.)

Explanation / Answer

as the estimate of proportion is not given

Let p is estimate proportion, then , we know that 95% Z is 1.96

        Z0.05/2*(p*(1-p)/n)1/2 = 0.025 => 1.96*(p*(1-p)/n)1/2 = 0.025

while for p*(1-p), when p=1/2, p*(1-p) arrive maximum and maximum value is ¼, so n =6146.56*1/4 =1537

So if no estimate were available for the proportion, we need 1537 sample size.

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